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A Third-Order Differential Equation and Starlikeness of a Double Integral Operator
- Source :
- Abstract and Applied Analysis, Vol 2011 (2011)
- Publication Year :
- 2011
- Publisher :
- Wiley, 2011.
-
Abstract
- Functions f(z)=z+∑2∞anzn that are analytic in the unit disk and satisfy the differential equation f'(z)+αzf''(z)+γz2f'''(z)=g(z) are considered, where g is subordinated to a normalized convex univalent function h. These functions f are given by a double integral operator of the form f(z)=∫01∫01G(ztμsν)t-μs-νds dt with G' subordinated to h. The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function h.
- Subjects :
- Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 10853375 and 16870409
- Volume :
- 2011
- Database :
- Directory of Open Access Journals
- Journal :
- Abstract and Applied Analysis
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.9f179b8a0ac048e9baecb9879fd8ca59
- Document Type :
- article
- Full Text :
- https://doi.org/10.1155/2011/901235